Three different topics have been studied under this project: (a) we have developed a new and improved procedure for generating circular ring configurations (of the freely jointed model of DNA) and we have estimated the ring-to-chain ratios of radii of gyration and sedimentation coefficients at infinite molecular weight and compared the results with those obtained by the so-called epsilon-method; (b) we have proved that the McGhee-von hippel theory is exact from a statistical mechanical view point, using the matrix method, and we have devised a new type of isotherm plot that can establish the mechanism of binding in cases not amenable to other existing plots; and (c) we have used the concept of once-visited sites in random walk theory to study isotope exchange experiments in biopolymers that undergo a helix-coil transition, and in F-actin or microtubules that undergo head-to-tail polymerization.